From 86bd52e15ee27f402178df3ab7915dbbf09ab3a8 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 21 Jan 2008 18:14:06 +0000 Subject: [PATCH] Added new graphs plus the code to generate them. [SVN r42900] --- .../distributions/nc_chi_squared.qbk | 4 +- doc/sf_and_dist/expint.qbk | 4 + doc/sf_and_dist/graphs/dist_graphs.cpp | 12 +- doc/sf_and_dist/graphs/expint2.png | Bin 0 -> 43254 bytes doc/sf_and_dist/graphs/expint_i.png | Bin 0 -> 21224 bytes doc/sf_and_dist/graphs/nccs_pdf.png | Bin 0 -> 61038 bytes doc/sf_and_dist/graphs/sf_graphs.cpp | 416 ++++++++++++++++++ doc/sf_and_dist/graphs/zeta1.png | Bin 0 -> 22815 bytes doc/sf_and_dist/graphs/zeta2.png | Bin 0 -> 22885 bytes doc/sf_and_dist/zeta.qbk | 4 + 10 files changed, 432 insertions(+), 8 deletions(-) create mode 100644 doc/sf_and_dist/graphs/expint2.png create mode 100644 doc/sf_and_dist/graphs/expint_i.png create mode 100644 doc/sf_and_dist/graphs/nccs_pdf.png create mode 100644 doc/sf_and_dist/graphs/sf_graphs.cpp create mode 100644 doc/sf_and_dist/graphs/zeta1.png create mode 100644 doc/sf_and_dist/graphs/zeta2.png diff --git a/doc/sf_and_dist/distributions/nc_chi_squared.qbk b/doc/sf_and_dist/distributions/nc_chi_squared.qbk index 018390039..11fd6a0f1 100644 --- a/doc/sf_and_dist/distributions/nc_chi_squared.qbk +++ b/doc/sf_and_dist/distributions/nc_chi_squared.qbk @@ -63,9 +63,9 @@ where ['f(x;k)] is the central chi squared distribution PDF, and ['I[sub v](x)] is a modified Bessel function of the first kind. The following graph illustrates how the distribution changes -for different values of [nu]: +for different values of [lambda]: -[$../graphs/nc_chi_square.png] +[$../graphs/nccs_pdf.png] [h4 Member Functions] diff --git a/doc/sf_and_dist/expint.qbk b/doc/sf_and_dist/expint.qbk index 6e7790b77..3c6a8572b 100644 --- a/doc/sf_and_dist/expint.qbk +++ b/doc/sf_and_dist/expint.qbk @@ -36,6 +36,8 @@ of z: [equation expint_n_1] +[$../graphs/expint2.png] + [h4 Accuracy] The following table shows the peak errors (in units of epsilon) @@ -135,6 +137,8 @@ of z: [equation expint_i_1] +[$../graphs/expint_i.png] + [h4 Accuracy] The following table shows the peak errors (in units of epsilon) diff --git a/doc/sf_and_dist/graphs/dist_graphs.cpp b/doc/sf_and_dist/graphs/dist_graphs.cpp index f0f45faa8..88e8ee804 100644 --- a/doc/sf_and_dist/graphs/dist_graphs.cpp +++ b/doc/sf_and_dist/graphs/dist_graphs.cpp @@ -229,12 +229,12 @@ int main() distribution_plotter nc_cs_plotter; - nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 0), "v=20, l=0"); - nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 1), "v=20, l=1"); - nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 5), "v=20, l=5"); - nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 10), "v=20, l=10"); - nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 20), "v=20, l=20"); - nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 100), "v=20, l=100"); + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 0), "v=20, λ=0"); + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 1), "v=20, λ=1"); + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 5), "v=20, λ=5"); + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 10), "v=20, λ=10"); + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 20), "v=20, λ=20"); + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 100), "v=20, λ=100"); nc_cs_plotter.plot("Non Central Chi Squared PDF", "nccs_pdf.svg"); distribution_plotter > diff --git a/doc/sf_and_dist/graphs/expint2.png b/doc/sf_and_dist/graphs/expint2.png new file mode 100644 index 0000000000000000000000000000000000000000..7ec13242cd231323abdc7a6039377408aa91482b GIT binary patch literal 43254 zcmeAS@N?(olHy`uVBq!ia0y~yU}|7sU|h|?#=yW3;HT!zz`(##?Bp53!NI{%!;#X# zz`(#+;1OBOz`%C|gc+x5^GP!>Fi4iTMwA5SrEaktG3U+Q^a#=G_gFu;x?2efh_JFqH$@yw=uJAp)TK7|6$y;i9ZepS7b&>@+9S{L{F%q}VhM{i_dlO$H{P87 zzO+I5fBE?{a;oQ_-ewUH6ch~HyO4`v-evp7Wo^4|M0Rv^ba?b_DlXcX^m^YSrhs5) zS>6Z+AwfaGtK6rO*cFtNlori8$~2*)qhrOqL`Dx67nhLp8yHlSl$2JbLlqk9Fm!fw zbi9%jYjAOKarw%_?EunN)yAp-vd{J~b+iYHS~CRJ1_cB(9PgK(e*4(5V{EHd{h6N@ zxh{S`pQFHqt=ZSL=35s(^U27{O1io#^yxNlKR>skqD@!!9qW~L_V-_ZD*2l0x^?R$ z%yJ~`e!tmVbUQUYU0F+O)tSd$US1hjS557?EI3i;L%if7sVTE&b(!VfnsWQu&(F^d z%+1#?blH0O-QC?AtH0;{`0?Ywg$n_%Zm7?%Y1*^L#>L$|eCPcG2OKi8v%_!X9d6_O z@$tC)(r<6??iPQ1tatUL3QbK-3A-8#HUD`%A0HnNe;Kopqp86-{oH|T*R~znR{s88 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b/doc/sf_and_dist/graphs/sf_graphs.cpp @@ -0,0 +1,416 @@ +#include +#include +#include +#include +#include +#include +#include +#include +#include + +class function_arity1_plotter +{ +public: + function_arity1_plotter() : m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0), m_has_legend(false) {} + + void add(boost::function f, double a, double b, const std::string& name) + { + if(name.size()) + m_has_legend = true; + // + // Now set our x-axis limits: + // + if(m_max_x == m_min_x) + { + m_max_x = b; + m_min_x = a; + } + else + { + if(a < m_min_x) + m_min_x = a; + if(b > m_max_x) + m_max_x = b; + } + m_points.push_back(std::pair >(name, std::map())); + std::map& points = m_points.rbegin()->second; + double interval = (b - a) / 200; + for(double x = a; x <= b; x += interval) + { + // + // Evaluate the function, set the Y axis limits + // if needed and then store the pair of points: + // + double y = f(x); + if((m_min_y == m_max_y) && (m_min_y == 0)) + m_min_y = m_max_y = y; + if(m_min_y > y) + m_min_y = y; + if(m_max_y < y) + m_max_y = y; + points[x] = y; + } + } + + void add(const std::map& m, const std::string& name) + { + if(name.size()) + m_has_legend = true; + m_points.push_back(std::pair >(name, m)); + std::map::const_iterator i = m.begin(); + + while(i != m.end()) + { + if((m_min_x == m_min_y) && (m_min_y == 0)) + { + m_min_x = m_max_x = i->first; + } + if(i->first < m_min_x) + { + m_min_x = i->first; + } + if(i->first > m_max_x) + { + m_max_x = i->first; + } + + if((m_min_y == m_max_y) && (m_min_y == 0)) + { + m_min_y = m_max_y = i->second; + } + if(i->second < m_min_y) + { + m_min_y = i->second; + } + if(i->second > m_max_y) + { + m_max_y = i->second; + } + + ++i; + } + } + + void plot(const std::string& title, const std::string& file, + const std::string& x_lable = std::string(), + const std::string& y_lable = std::string()) + { + using namespace boost::svg; + + static const svg_color colors[5] = + { + darkblue, + darkred, + darkgreen, + darkorange, + chartreuse + }; + + svg_2d_plot plot; + plot.image_size(600, 400); + plot.copyright_holder("John Maddock").copyright_date("2008").boost_license_on(true); + plot.coord_precision(4); // Ciould be 3 for smaller plots. + plot.title(title).legend_title_font_size(15).title_on(true); + plot.legend_on(m_has_legend); + + double x_delta = (m_max_x - m_min_x) / 50; + double y_delta = (m_max_y - m_min_y) / 50; + plot.x_range(m_min_x, m_max_x + x_delta) + .y_range(m_min_y, m_max_y + y_delta); + plot.x_label_on(true).x_label(x_lable); + plot.y_label_on(true).y_label(y_lable); + plot.y_major_grid_on(false).x_major_grid_on(false); + plot.x_num_minor_ticks(3); + plot.y_num_minor_ticks(3); + // + // Work out axis tick intervals: + // + double l = std::floor(std::log10((m_max_x - m_min_x) / 10) + 0.5); + double interval = std::pow(10.0, (int)l); + if(((m_max_x - m_min_x) / interval) > 10) + interval *= 5; + plot.x_major_interval(interval); + l = std::floor(std::log10((m_max_y - m_min_y) / 10) + 0.5); + interval = std::pow(10.0, (int)l); + if(((m_max_y - m_min_y) / interval) > 10) + interval *= 5; + plot.y_major_interval(interval); + plot.plot_window_on(true); + plot.plot_border_color(lightslategray).legend_border_color(lightslategray).background_border_color(lightslategray); + + int color_index = 0; + + for(std::list > >::const_iterator i = m_points.begin(); + i != m_points.end(); ++i) + { + plot.plot(i->second, i->first) + .line_on(true) + .line_color(colors[color_index]) + .line_width(0.5) + .shape(none); + if(i->first.size()) + ++color_index; + color_index = color_index % (sizeof(colors)/sizeof(colors[0])); + } + plot.write(file); + } + + void clear() + { + m_points.clear(); + m_min_x = m_min_y = m_max_x = m_max_y = 0; + m_has_legend = false; + } + +private: + std::list > > m_points; + double m_min_x, m_max_x, m_min_y, m_max_y; + bool m_has_legend; +}; + +template +struct location_finder +{ + location_finder(F _f, double t, double x0) : f(_f), target(t), x_off(x0){} + + double operator()(double x) + { + try + { + return f(x + x_off) - target; + } + catch(const std::overflow_error&) + { + return boost::math::tools::max_value(); + } + catch(const std::domain_error&) + { + if(x + x_off == x_off) + return f(x_off + boost::math::tools::epsilon() * x_off); + throw; + } + } + +private: + F f; + double target; + double x_off; +}; + +template +double find_end_point(F f, double x0, double target, bool rising, double x_off = 0) +{ + boost::math::tools::eps_tolerance tol(50); + boost::uintmax_t max_iter = 1000; + return boost::math::tools::bracket_and_solve_root( + location_finder(f, target, x_off), + x0, + double(1.5), + rising, + tol, + max_iter).first; +} + +double sqrt1pm1(double x) +{ + return boost::math::sqrt1pm1(x); +} + +double lbeta(double a, double b) +{ + return std::log(boost::math::beta(a, b)); +} + +int main() +{ + function_arity1_plotter plot; + double (*f)(double); + double (*f2)(double, double); + double (*f2u)(unsigned, double); + double (*f2i)(int, double); + double (*f3)(double, double, double); + + f = boost::math::zeta; + plot.add(f, 1 + find_end_point(f, 0.1, 40.0, false, 1.0), 10, ""); + plot.add(f, -20, 1 + find_end_point(f, -0.1, -40.0, false, 1.0), ""); + plot.plot("Zeta Function Over [-20,10]", "zeta1.svg", "z", "zeta(z)"); + + plot.clear(); + plot.add(f, -14, 0, ""); + plot.plot("Zeta Function Over [-14,0]", "zeta2.svg", "z", "zeta(z)"); + + f = boost::math::tgamma; + double max_val = f(6); + plot.clear(); + plot.add(f, find_end_point(f, 0.1, max_val, false), 6, ""); + plot.add(f, -1 + find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, -max_val, false), ""); + plot.add(f, -2 + find_end_point(f, 0.1, max_val, false, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), ""); + plot.add(f, -3 + find_end_point(f, 0.1, -max_val, true, -3), -2 + find_end_point(f, -0.1, -max_val, false, -2), ""); + plot.add(f, -4 + find_end_point(f, 0.1, max_val, false, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), ""); + plot.plot("tgamma", "tgamma.svg", "z", "tgamma(z)"); + + f = boost::math::lgamma; + max_val = f(10); + plot.clear(); + plot.add(f, find_end_point(f, 0.1, max_val, false), 10, ""); + plot.add(f, -1 + find_end_point(f, 0.1, max_val, false, -1), find_end_point(f, -0.1, max_val, true), ""); + plot.add(f, -2 + find_end_point(f, 0.1, max_val, false, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), ""); + plot.add(f, -3 + find_end_point(f, 0.1, max_val, false, -3), -2 + find_end_point(f, -0.1, max_val, true, -2), ""); + plot.add(f, -4 + find_end_point(f, 0.1, max_val, false, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), ""); + plot.add(f, -5 + find_end_point(f, 0.1, max_val, false, -5), -4 + find_end_point(f, -0.1, max_val, true, -4), ""); + plot.plot("lgamma", "lgamma.svg", "z", "lgamma(z)"); + + f = boost::math::digamma; + max_val = 10; + plot.clear(); + plot.add(f, find_end_point(f, 0.1, -max_val, true), 10, ""); + plot.add(f, -1 + find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, max_val, true), ""); + plot.add(f, -2 + find_end_point(f, 0.1, -max_val, true, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), ""); + plot.add(f, -3 + find_end_point(f, 0.1, -max_val, true, -3), -2 + find_end_point(f, -0.1, max_val, true, -2), ""); + plot.add(f, -4 + find_end_point(f, 0.1, -max_val, true, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), ""); + plot.plot("digamma", "digamma.svg", "z", "digamma(z)"); + + f = boost::math::erf; + plot.clear(); + plot.add(f, -3, 3, ""); + plot.plot("erf", "erf.svg", "z", "erf(z)"); + f = boost::math::erfc; + plot.clear(); + plot.add(f, -3, 3, ""); + plot.plot("erfc", "erfc.svg", "z", "erfc(z)"); + + f = boost::math::erf_inv; + plot.clear(); + plot.add(f, -1 + find_end_point(f, 0.1, -3, true, -1), 1 + find_end_point(f, -0.1, 3, true, 1), ""); + plot.plot("erf_inv", "erf_inv.svg", "z", "erf_inv(z)"); + f = boost::math::erfc_inv; + plot.clear(); + plot.add(f, find_end_point(f, 0.1, 3, false), 2 + find_end_point(f, -0.1, -3, false, 2), ""); + plot.plot("erfc_inv", "erfc_inv.svg", "z", "erfc_inv(z)"); + + f = boost::math::log1p; + plot.clear(); + plot.add(f, -1 + find_end_point(f, 0.1, -10, true, -1), 10, ""); + plot.plot("log1p", "log1p.svg", "z", "log1p(z)"); + + f = boost::math::expm1; + plot.clear(); + plot.add(f, -4, 2, ""); + plot.plot("expm1", "expm1.svg", "z", "expm1(z)"); + + f = boost::math::cbrt; + plot.clear(); + plot.add(f, -10, 10, ""); + plot.plot("cbrt", "cbrt.svg", "z", "cbrt(z)"); + + f = sqrt1pm1; + plot.clear(); + plot.add(f, -1 + find_end_point(f, 0.1, -10, true, -1), 5, ""); + plot.plot("sqrt1pm1", "sqrt1pm1.svg", "z", "sqrt1pm1(z)"); + + f = boost::math::sinc_pi; + plot.clear(); + plot.add(f, -10, 10, ""); + plot.plot("sinc_pi", "sinc_pi.svg", "z", "sinc_pi(z)"); + + f = boost::math::sinhc_pi; + plot.clear(); + plot.add(f, -5, 5, ""); + plot.plot("sinhc_pi", "sinhc_pi.svg", "z", "sinhc_pi(z)"); + + f = boost::math::acosh; + plot.clear(); + plot.add(f, 1, 10, ""); + plot.plot("acosh", "acosh.svg", "z", "acosh(z)"); + + f = boost::math::asinh; + plot.clear(); + plot.add(f, -10, 10, ""); + plot.plot("asinh", "asinh.svg", "z", "asinh(z)"); + + f = boost::math::atanh; + plot.clear(); + plot.add(f, -1 + find_end_point(f, 0.1, -5, true, -1), 1 + find_end_point(f, -0.1, 5, true, 1), ""); + plot.plot("atanh", "atanh.svg", "z", "atanh(z)"); + + f2 = boost::math::tgamma_delta_ratio; + plot.clear(); + plot.add(boost::bind(f2, _1, -0.5), 1, 40, "delta = -0.5"); + plot.add(boost::bind(f2, _1, -0.2), 1, 40, "delta = -0.2"); + plot.add(boost::bind(f2, _1, -0.1), 1, 40, "delta = -0.1"); + plot.add(boost::bind(f2, _1, 0.1), 1, 40, "delta = 0.1"); + plot.add(boost::bind(f2, _1, 0.2), 1, 40, "delta = 0.2"); + plot.add(boost::bind(f2, _1, 0.5), 1, 40, "delta = 0.5"); + plot.add(boost::bind(f2, _1, 1.0), 1, 40, "delta = 1.0"); + plot.plot("tgamma_delta_ratio", "tgamma_delta_ratio.svg", "z", "tgamma_delta_ratio(delta, z)"); + + f2 = boost::math::gamma_p; + plot.clear(); + plot.add(boost::bind(f2, 0.5, _1), 0, 20, "a = 0.5"); + plot.add(boost::bind(f2, 1.0, _1), 0, 20, "a = 1.0"); + plot.add(boost::bind(f2, 5.0, _1), 0, 20, "a = 5.0"); + plot.add(boost::bind(f2, 10.0, _1), 0, 20, "a = 10.0"); + plot.plot("gamma_p", "gamma_p.svg", "z", "gamma_p(a, z)"); + + f2 = boost::math::gamma_q; + plot.clear(); + plot.add(boost::bind(f2, 0.5, _1), 0, 20, "a = 0.5"); + plot.add(boost::bind(f2, 1.0, _1), 0, 20, "a = 1.0"); + plot.add(boost::bind(f2, 5.0, _1), 0, 20, "a = 5.0"); + plot.add(boost::bind(f2, 10.0, _1), 0, 20, "a = 10.0"); + plot.plot("gamma_q", "gamma_q.svg", "z", "gamma_q(a, z)"); + + f2 = lbeta; + plot.clear(); + plot.add(boost::bind(f2, 0.5, _1), 0.00001, 5, "a = 0.5"); + plot.add(boost::bind(f2, 1.0, _1), 0.00001, 5, "a = 1.0"); + plot.add(boost::bind(f2, 5.0, _1), 0.00001, 5, "a = 5.0"); + plot.add(boost::bind(f2, 10.0, _1), 0.00001, 5, "a = 10.0"); + plot.plot("beta", "beta.svg", "z", "log(beta(a, z))"); + + f = boost::math::expint; + max_val = f(4); + plot.clear(); + plot.add(f, find_end_point(f, 0.1, -max_val, true), 4, ""); + plot.add(f, -3, find_end_point(f, -0.1, -max_val, false), ""); + plot.plot("Exponential Integral Ei", "expint_i.svg", "z", "expint(z)"); + + f2u = boost::math::expint; + max_val = 1; + plot.clear(); + plot.add(boost::bind(f2u, 1, _1), find_end_point(boost::bind(f2u, 1, _1), 0.1, max_val, false), 2, "n = 1 "); + plot.add(boost::bind(f2u, 2, _1), find_end_point(boost::bind(f2u, 2, _1), 0.1, max_val, false), 2, "n = 2 "); + plot.add(boost::bind(f2u, 3, _1), 0, 2, "n = 3 "); + plot.add(boost::bind(f2u, 4, _1), 0, 2, "n = 4 "); + plot.plot("Exponential Integral En", "expint2.svg", "z", "expint(n, z)"); + + f3 = boost::math::ibeta; + plot.clear(); + plot.add(boost::bind(f3, 9, 1, _1), 0, 1, "a = 9, b = 1"); + plot.add(boost::bind(f3, 7, 2, _1), 0, 1, "a = 7, b = 2"); + plot.add(boost::bind(f3, 5, 5, _1), 0, 1, "a = 1, b = 1"); + plot.add(boost::bind(f3, 2, 7, _1), 0, 1, "a = 2, b = 7"); + plot.add(boost::bind(f3, 1, 9, _1), 0, 1, "a = 1, b = 9"); + plot.plot("ibeta", "ibeta.svg", "z", "ibeta(a, b, z)"); + + f2i = boost::math::legendre_p; + plot.clear(); + plot.add(boost::bind(f2i, 1, _1), -1, 1, "l = 1"); + plot.add(boost::bind(f2i, 2, _1), -1, 1, "l = 2"); + plot.add(boost::bind(f2i, 3, _1), -1, 1, "l = 3"); + plot.add(boost::bind(f2i, 4, _1), -1, 1, "l = 4"); + plot.add(boost::bind(f2i, 5, _1), -1, 1, "l = 5"); + plot.plot("Legendre Polynomials", "legendre_p.svg", "x", "legendre_p(l, x)"); + + f2u = boost::math::legendre_q; + plot.clear(); + plot.add(boost::bind(f2u, 1, _1), -0.95, 0.95, "l = 1"); + plot.add(boost::bind(f2u, 2, _1), -0.95, 0.95, "l = 2"); + plot.add(boost::bind(f2u, 3, _1), -0.95, 0.95, "l = 3"); + plot.add(boost::bind(f2u, 4, _1), -0.95, 0.95, "l = 4"); + plot.add(boost::bind(f2u, 5, _1), -0.95, 0.95, "l = 5"); + plot.plot("Legendre Polynomials of the Second Kind", "legendre_q.svg", "x", "legendre_q(l, x)"); + + return 0; +} + diff --git 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zxPj{&BMZY}P*z{GNJ%$-UyQK2pNTAc18V>ST*wf? z!YaVPqot=8mXWdI+WPo>D=r4^hcXTf1}R6oL~re_-tOh?Eh;RWY{kdGy^w*afe|#j zF-g_Csosvdj&x8#!1&T^`)!AS8^)2v#gw4ynAX3EuothJk_MgHic&?#WA* lU;o#B5!5mKF!w+Er)je;Z+*kJje&uI!PC{xWt~$(698@7T{Zv! literal 0 HcmV?d00001 diff --git a/doc/sf_and_dist/zeta.qbk b/doc/sf_and_dist/zeta.qbk index 0ccc7fe26..b14eb938e 100644 --- a/doc/sf_and_dist/zeta.qbk +++ b/doc/sf_and_dist/zeta.qbk @@ -34,6 +34,10 @@ of z: [equation zeta1] +[$../graphs/zeta1.png] + +[$../graphs/zeta2.png] + [h4 Accuracy] The following table shows the peak errors (in units of epsilon)